United Airlines is not planning to shut down its pet transportation service but will continue its review of the program, the airline's CEO, Oscar Munoz, told CNBC Wednesday.

A day earlier United halted new reservations for the service as it conducts a review following a week of incidents involving travelers' pets, including the death of a French bulldog puppy named Kokito, whose carrier was placed in an overhead bin. After that several dogs were sent to the wrong destinations, including a German shepherd that United mistakenly sent to Japan instead of Kansas City.

"We are always going to review all the different options," Munoz said in an interview. There are other things the airline could do before shutting the program down entirely, he said, pointing to the fact that certain "animals are more high-risk" than others.

"Doing away with something would be the simplest thing to do," Munoz said. "That's not what we're going to do. That's not what United's about."

Munoz said the pet transportation program counts military families and animal breeders among its clients.

United transports more animals in its cargo hold than any other U.S. airline and had 18 of the 24 deaths reported last year, according to the U.S. Department of Transportation.